The orientation of crystals in liquid crystalline polymers (LCPs) during the processing method affects the properties of these materials. In this paper, the main components of modeling the directionality of LCPs, name...The orientation of crystals in liquid crystalline polymers (LCPs) during the processing method affects the properties of these materials. In this paper, the main components of modeling the directionality of LCPs, namely Franks elastic energy equation, evolution equation and translation of directors are studied. The complexity of flow channels in polymer processing requires a more robust method for modeling directionality that can be applied to varieties of meshes. A method for practically simulating the directionality of crystallines on a macroscopic scale is developed. This method can be applied to any combination and type of meshes. The results show successful modeling of the directionality for each component of the model. Here, a 2D case with structured and unstructured mesh is considered and the rheology is simulated using ANSYS? FLUENT?. C++ codes written for user defined functions (UDFs) are used to implement the directionality simulation.展开更多
Frank’s theory describes that a screw dislocation will produce a pit on the surface,and has been evidenced in many material systems including GaN.However,the size of the pit calculated from the theory deviates signif...Frank’s theory describes that a screw dislocation will produce a pit on the surface,and has been evidenced in many material systems including GaN.However,the size of the pit calculated from the theory deviates significantly from experimental result.Through a careful observation of the variations of surface pits and local surface morphology with growing temperature and V/III ratio for c-plane GaN,we believe that Frank’s model is valid only in a small local surface area where thermodynamic equilibrium state can be assumed to stay the same.If the kinetic process is too vigorous or too slow to reach a balance,the local equilibrium range will be too small for the center and edge of the screw dislocation spiral to be kept in the same equilibrium state.When the curvature at the center of the dislocation core reaches the critical value 1/r0,at the edge of the spiral,the accelerating rate of the curvature may not fall to zero,so the pit cannot reach a stationary shape and will keep enlarging under the control of minimization of surface energy to result in a large-sized surface pit.展开更多
文摘The orientation of crystals in liquid crystalline polymers (LCPs) during the processing method affects the properties of these materials. In this paper, the main components of modeling the directionality of LCPs, namely Franks elastic energy equation, evolution equation and translation of directors are studied. The complexity of flow channels in polymer processing requires a more robust method for modeling directionality that can be applied to varieties of meshes. A method for practically simulating the directionality of crystallines on a macroscopic scale is developed. This method can be applied to any combination and type of meshes. The results show successful modeling of the directionality for each component of the model. Here, a 2D case with structured and unstructured mesh is considered and the rheology is simulated using ANSYS? FLUENT?. C++ codes written for user defined functions (UDFs) are used to implement the directionality simulation.
文摘为解决目前交通分配中存在的不确定性问题,基于Wardrop用户平衡原理,利用起讫点(OD,Origin Destination)估计方法和Beckman交通分配模型,建立了一种交通分配不确定性计算方法.该方法分别以不同置信水平下的OD估计结果的上下限为输入量,然后利用Frank-Wolf算法求解交通分配模型,得到不同置信水平下的路段流量区间,以此量化交通分配问题中的不确定性.以南京市区域路网为研究对象进行案例分析,并采用宽度流量比 R 和无效覆盖率(Kickoff Percentage,KP)对模型结果进行评价,结果表明该方法可以得到路段流量的置信区间,量化交通分配的不确定性.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11204009 and 61204011)the Beijing Municipal Natural Science Foundation,China(Grant No.4142005)
文摘Frank’s theory describes that a screw dislocation will produce a pit on the surface,and has been evidenced in many material systems including GaN.However,the size of the pit calculated from the theory deviates significantly from experimental result.Through a careful observation of the variations of surface pits and local surface morphology with growing temperature and V/III ratio for c-plane GaN,we believe that Frank’s model is valid only in a small local surface area where thermodynamic equilibrium state can be assumed to stay the same.If the kinetic process is too vigorous or too slow to reach a balance,the local equilibrium range will be too small for the center and edge of the screw dislocation spiral to be kept in the same equilibrium state.When the curvature at the center of the dislocation core reaches the critical value 1/r0,at the edge of the spiral,the accelerating rate of the curvature may not fall to zero,so the pit cannot reach a stationary shape and will keep enlarging under the control of minimization of surface energy to result in a large-sized surface pit.
